Research On The Fluctuation Of House Price And Rental Price In Nanjing City Based On Statistical Modeling

This paper selects monthly house prices and rents series from June 2010 to June 2016 in Nanjing as sample data.First,we establish the MS model and ARIMA model to study the volatility of housing prices in Nanjing from long term and short term.Then,we establish the MS rent volatility model combined with the HP filtering method to analyze the volatility and intrinsic growth characteristics of the rent.Finally,we establish the SVAR model to study the dynamic cooperation relationship between house price and rent in Nanjing.In view of the price fluctuation,we establish the house price MS model(2.3)to obtain the classification criterion of high and low volatility and the matrix of state transition probability.The parameters were estimated by the Hamilton maximum likelihood method.From the matrix,high volatility and low volatility are 0.987 and 0.986 respectively.Their duration are 74.6 months and 68.99 months.Now the house price is in a high volatility.Through the study of the ergodic and stationary distribution of house price Markov chain,the probability of house price stability at high and low volatility are 0.4815 and 0.5186 after a long period of time.Then,we eventually choose the ARIMA(2,2,2)model to predict the house price from July 2016 to December 2016 in Nanjing.The result shows that the house prices will continue to show an upward trend in the next few months.Compared with the latest published price index of China Index Research Institute,the predicted values of July and August are 18290 and 18913,the relative error of these two months predicted values were 1.1% and 1.3%.In view of the rent fluctuation,we establish the rent MS model(3.1)and use EM algorithm for estimating transition probability matrix.From the matrix,high volatility and low volatility are 0.9347 and 0.9184 respectively.Their duration are 15.3 months and 12.3months.Now the rent price is in a low volatility.After a long period of time the probability of house price stability at high and low volatility are 0.5555 and 0.4445.HP filter method appears that the actual observation of the growth rate is far greater than the internal growth.Besides,the measured long-term equilibrium rent growth shows that rent volatility began to increase.The volatility cycle begins to pull up to 26 months which will still continue.Combined with the actual rents,rents are still rising which has a close contact with the destocking policy for the first tier cities.Concerning the dynamic cooperative relationship between house price and rent,we use WCC constraints to identify the model(4.25)and(4.26),the parameters of the model were obtained by using the FIMLE method.Then we use the impulse response and variance decomposition based on SVAR model to study the dynamic cooperativerelationship between house price and rent.The research shows that house prices has a significant positive impact on the rent both in the short term and long term.But rents do not cause any fluctuations in house prices in short term and have a negative impact on the price of housing in the long run.The impact of housing prices on rent is much stronger than the impact of the rent on price.From the point of view of the variance decomposition of rents,rents and house prices as endogenous variables of the contribution to the house price become smooth after 10 th period.About 87% of the impact comes from housing prices,13% of the impact from the rental.For rent,about 29% of the impact comes from housing prices,71% of the impact from the rental itself.Finally,this paper gives reasonable references to the government and the home buyers,especially college students.